A point is chosen at random from the points on the interval

A point is chosen at random from the points on the interval (0,1), and a second point is then chosen at random from the points between the first point and 1. What is the expected distance of second point from zero, while the first point has a distance of 0.3 from zero? (Please enter your answer in x.xx format)

Solution

X1 ~ U(0 ,1)

Therefore X2 ~ U(x1 , 1)

E(X2 | x1 = 0.3) = (1 - 0.3)/2. = 0.35